The lazy regime developed in this work draws from and overlaps with these existing techniques to a great extent.
It naturally incorporates the clear/compress/twist optimization and the short-circuiting technique associated with certain Morse vector fields, as described in §REF . The decomposition procedures presented in Algorithms  and  are nearly identical, mathematically, to the cohomology algorithm, which applies the standard algorithm to the antitranspose of \(D\) ; the primary functional difference lies only with the type of information that is stored versus discarded on each iteration. Moreover, the use of lazy data structures in these algorithms follows from the pioneering example of [1]}, which was also a source of broader inspiration for this work. Finally, many of the concepts introduced in our discussion have immediate analogs for \(R = DV\)  decomposition, which were largely worked out in [2]}.
